This application is based upon and claims the benefit of priority from the prior Japanese Patent Application No. 11-258777, filed Sep. 13, 1999, the entire contents of which are incorporated herein by reference.
The present invention relates to a nuclear medical diagnosis apparatus and image reconstruction method therefor, wherein gamma rays emitted from radioisotopes (RIs) administered to a target object are detected from many directions, and the RIs density distribution is generated on the basis of detection data (projection data).
Many systems are commercially available, which can generate not only a planar image upon projecting an RIs density distribution in one direction but also the density distribution of slices of a target object, like X-ray computer tomography apparatuses. Techniques for imaging the slice density distributions are classified into SPECT (Single Photon Emission Computed Tomography) and PET (Positron Emission computed Tomography) depending on the nuclides.
In SPECT, a single photon nuclide is administered to the target object. To count the number of photons, a gamma ray emitted from the single photon nuclide is detected. A detector is rotated through a small angle, and the gamma ray is counted at this rotation position again. The gamma ray is repeatedly counted at many positions while the detector is rotated step by step. The density distribution in the slice is reconstructed by calculating the multi-directional projection data acquired by repeating the counting operation. In PET, a positron nuclide is administered to the target object. Two photons generated when the positron emitted by the positron nuclide combines with a neighboring negative electron and disappears are simultaneously counted to reconstruct the nuclide density distribution in the slice.
FIG. 1 is a schematic view showing the arrangement of a detector used in a conventional nuclear medical diagnosis apparatus. A detector 1 has a function of measuring the incident position of a gamma ray and its energy in real time. A thick lead plate formed with a plurality of small holes densely, i.e., collimator 2 is arranged on the detection surface of the detector 1. The collimator 2 can be of a parallel hole type in which the holes are parallel to each other and perpendicular to the detection surface, a slant hole type in which the holes are parallel to each other and slant with respect to the detection surface, a diverging type in which the holes are formed in an outwardly diverging pattern, or a converging type in which the holes are formed in a pattern having a focal point formed outside the collimator. The parallel hole type collimator is exemplified here.
One photon of a gamma ray passing through the collimator 2 is incident on a scintillator 3 of several ten cm square and converted into several thousand to several ten-thousand low-energy photons. These photons are detected by a number of photomultiplier tubes (PMTs) 4. The incident position of the gamma ray can be calculated with a precision of about 3 mm by comparing the output levels of the PMTs 4. This allows measuring projection data obtained by projecting an RIs 3D concentration distribution in the target object on a 2D plane. This measurement operation is repeated for the target object at various angular positions. As in the X-ray CT apparatus, images are reconstructed on the basis of the projection data to simultaneously acquire a large number of tomographic images.
As shown in FIG. 2, to move the detector along the track nearest to the target object O, the distance (rotation radius) D(xcex8) between rotation center C of the detector 1 and the detection surface 1a changes depending on the rotational angle xcex8.
In the SPECT apparatus, the detector 1 can measure the 2D projection data, and the 3D RI concentration distribution f(x,y,z) can be calculated on the basis of the measured projection data. To reconstruct an image, a slice (x-y plane) perpendicular to the rotational axis (body axis of the target object O, i.e., z-axis) is regarded as the reconstructing unit. Image reconstruction is essentially a 2D process.
From the RI density distribution f(x, y) in the target object O, projection data p(r, xcex8) is represented by:       p    ⁢          (              r        ,        θ            )        =            ∫              -        ∞            ∞        ⁢                  f        ⁢                  (                      x            ,            y                    )                    ⁢              xe2x80x83            ⁢              ⅆ        s            
where r is the distance from the rotation center C to a projection ray L defining the direction of the collimator 2 and where in FIG. 2, the integration along the projection ray L is indicated by ƒ ds (i.e., the component orthogonal to r is represented by s).
Since integration is performed along the projection ray L, we have:                               [                      xe2x80x83                    ⁢                                                    x                                                                    y                                              ⁢                      xe2x80x83                    ]                =                              [                                                                                cos                    ⁢                                          xe2x80x83                                        ⁢                    θ                                                                                                              -                      sin                                        ⁢                                          xe2x80x83                                        ⁢                    θ                                                                                                                    sin                    ⁢                                          xe2x80x83                                        ⁢                    θ                                                                                        cos                    ⁢                                          xe2x80x83                                        ⁢                    θ                                                                        ⁢                          xe2x80x83                        ]                    ⁢                      xe2x80x83                    [                                                    r                                                                    s                                              ⁢                      xe2x80x83                    ]                                    (        2        )            
The transform from the RI density distribution f to the projection data p by equation (2) is called projection transform P, which is expressed as p=Pf. This projection transform is also called a 2D radon transform. Orthogonal coordinates are set as  less than r, xcex8 greater than , and a space in which projection data p(r, xcex8) is plotted is called an  less than r, xcex8 greater than  space. This is also called a sinogram.
For example, a convolutional backprojection is used as a technique for calculating an RI density distribution f from the projection data p. This method is practiced in the following procedures.
The projection data p(r, xcex8) is convoluted with a reconstruction function h to obtain compensated projection data q(r, xcex8) given by:                               q          ⁡                      (                          r              ,              θ                        )                          =                              ∫                          -              ∞                        ∞                    ⁢                                    p              ⁡                              (                                  t                  ,                  θ                                )                                      ⁢                          h              ⁡                              (                                  r                  -                  t                                )                                      ⁢                          xe2x80x83                        ⁢                          ⅆ              t                                                          (        3        )            
The reconstruction function h is a generalized function and expressed as:                                           h            ⁡                          (              r              )                                =                                                    -                1                            /                              (                                  2                  ⁢                  π                  ⁢                                      xe2x80x83                                    ⁢                                      r                    2                                                  )                                      ⁢                          (                                                "LeftBracketingBar"                  r                  "RightBracketingBar"                                 greater than                 0                            )                                      ⁢                  
                ⁢                                            ∫                              -                ∞                            ∞                        ⁢                                          h                ⁡                                  (                  r                  )                                            ⁢                              xe2x80x83                            ⁢                              ⅆ                r                                              =          0                                    (        4        )            
In practice, a function hm(r) obtained by convoluting an appropriate smoothing function n(r) with the reconstruction function h(r) and given by:                                           h            m                    ⁡                      (            r            )                          =                              ∫                          -              ∞                        ∞                    ⁢                                    h              ⁡                              (                t                )                                      ⁢                          n              ⁡                              (                                  r                  -                  t                                )                                      ⁢                          xe2x80x83                        ⁢                          ⅆ              t                                                          (        5        )            
is used in place of the generalized function.
The corrected projection data q is backprojected by calculating:                               f          ⁡                      (                          x              ,              y                        )                          =                              1            π                    ⁢                                    ∫              0              π                        ⁢                                          q                ⁡                                  (                                                                                    x                        ⁢                                                  xe2x80x83                                                ⁢                        cos                        ⁢                                                  xe2x80x83                                                ⁢                        θ                                            +                                              y                        ⁢                                                  xe2x80x83                                                ⁢                        sin                        ⁢                                                  xe2x80x83                                                ⁢                        θ                                                              ,                    θ                                    )                                            ⁢                              xe2x80x83                            ⁢                              ⅆ                θ                                                                        (        6        )            
The backprojection is calculated by integrating points (x,y) on the RI density distribution. In practice, however, data fxcex8(x,y) (=q(xc3x97cos xcex8+ysin xcex8, xcex8)) transformed the corrected projection data q(r, xcex8) into (x,y) coordinates is generated and accumulated in units of rotation angles.
FIG. 3 shows the track of a gamma ray passing through one collimator hole in the parallel hole type collimator. The depth and width of one collimator hole are defined as b and a, respectively. Assume a gamma ray incident obliquely at an angle xcfx86 with respect to the axis of the collimator hole 2.
As is known well, a collimator has directivity for selectively transmitting only gamma rays incident from a specific direction. This directivity is not sharp but has an angle of divergence depending on the depth b and width a of the collimator hole 2. That is, the detector has sensitivity within the angle of divergence. In other words, the sensitivity is not zero within the angle of divergence (tan |xcfx86| greater than a/b). A maximum angle is represented xe2x80x9c"PHgr"xe2x80x9d, a minimum angle is represented xe2x80x9cxe2x88x92"PHgr"xe2x80x9d. When an incidence angle of gamma rays is within xe2x88x92"PHgr" to "PHgr", the detector has sensitivity for the gamma rays.
The sensitivity is the ratio of the area of the gamma ray arrival region to the area of the total region (AA+XX) of the detection channel. If the maximum sensitivity is 1, xcfx86xe2x89xa00, i.e., the obliquely incident gamma ray arrival region is AA, and the remaining region XX is a dead zone. The sensitivity is, therefore, given by AA/(AA+XX).
The detection sensitivity changes depending on the incident angle xcfx86, as shown in FIG. 4. This is called xe2x80x9cincident angle dependence of detection sensitivityxe2x80x9d. The incident angle dependence S(xcfx86) of detection sensitivity is represented by a function shown in FIG. 5. If |xcfx86| greater than "PHgr", then s(xcfx86)=0.
The angle of divergence thus decreases the resolution of the detector. A decrease in resolution increases as the distance d between the detection surface 1a and an RI position Op increases (distance dependence of resolution).
No practical technique has been proposed to date, which can effectively suppress any decrease in resolution and any distance dependence of resolution, which are caused by the fact the collimator directivity has a predetermined angle of divergence. In a theory, this can be formulated as a reverse solution. A method of solving a optimum solution can be obtained. But a large quantity of a calculation is needed to execute this method, this quantity is unreality in a practical use.
It is an object of the present invention to effectively suppress any decrease in resolution and any distance dependence of resolution which are caused by that fact collimator directivity has a certain angle of divergence in a nuclear medical diagnosis apparatus, and an image reconstruction method used in this apparatus.
A nuclear medical diagnosis apparatus according to the present invention comprises a detector configured to detect gamma rays emitted from radioisotopes administered to a target object, a mechanism configured to move the detector with respect to the target object, a correcting unit configured to correct projection data, detected by the detector, on the basis of other projection data detected at a plurality of positions associated with a line which passes through a detection position of the projection data and crosses a detection surface of the detector at a predetermined angle, and a unit configured to generate a radioisotope density distribution on the basis of the corrected projection data.
Additional objects and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objects and advantages of the invention may be realized and obtained by means of the instrumentalities and combinations particularly pointed out hereinafter.